A Study Of Modeling And Simulation Methods For Compressible Turbulent Flows Based On One-Dimensional Turbulence

"One-dimensional turbulence"(ODT)is an innovative modeling methodology which is able to capture the stochastic and multi-scale dynamics of turbulent flows.Based on the research background of modeling and simulation methods for high-speed flows,a systematic study is carried out to fulfill the whole procedures of comprehension,realization,and innovation for ODT related methods in compressible turbulence.In this dissertation,mathematic modeling,numerical tests and case validations are implemented to ensure the newly developed methods to obey the physics of compressible turbulent flows.First of all,the fundamental theory is carefully introduced.An introduction of canonical large eddy simulation(LES)method is given,and the limitations of LES is evaluated.ODT is a stochastic multi-scale model which aims at compensating the shortcomings of traditional LES.The theoretical basis of ODT is explicated based on the physcics of turbulent flows.The modeling method of ODT can be summed up in three aspects:the one-dimensional governing equations for solving the primary laminar flowfield,the one-dimensional eddy analogy to describe the turbulent eddies,and the stochastic sampling process to define the sizes and locations of eddies.After that,the study in current dissertation starts to focus on pratical numerical tests instead of theoretical introduction.The numerical realization of ODT is explained in detail.Incompressible channel flow cases with differnet Reynolds numbers have been implemented based on traditional incompressible ODT with Eulerian frame.Simulation results represent the accurately captured near-wall profiles,which is the major advantage of ODT.The test case of shock induced combustion from Dr.Zoltan Jozefik is reproduced,and drawbacks of the Lagrangian compressible ODT is concluded.Specifically speaking,the major limitations of Jozefik's compressible ODT lie in two aspects:nonconservative governing equations and a quasi incompressible solver.Finally,innovative studies are implemented.The modeling principles of compressible ODT is summarised,and a conservative compressible ODT method based on an Eulerian frame has been developed.Conservative compressible ODT governing equations have been deduced from three dimensional Navier-Stokes equations and the one-dimensional truncation assumption of ODT.A second order TVD shock capturing scheme is introduced into ODT,which is used to solve the advective terms in governing equations.Meanwhile,the one-dimensional eddy analogy is adjusted to fit the conservative form of governing equations.Time advancement schemes for different modules in ODT have also been adapted for compressible flow simulation.The new conservative compressible ODT method have been validated in detail,and its computational cost is also evaluated.A test of adjustable paramters in compressible ODT is carried out.The performance of conservative compressible ODT in advection-dominated shock-turbulence interaction problems is tested by Richtmyer-Meshkov instability cases.Results indicate that the introduction of a shock capturing scheme significantly improves the ODT model's performance in shock related flows.Profiles of turbulent kinetic energy(TKE)are qualitatively improved compared to results obtained from previous Lagrangian compressible ODT.The performance of conservative compressible ODT in diffusion-dominated wall-bounded turbulence is tested by isothermal-wall supersonic channel flow cases.In the near-wall region,profiles obtained by ODT nearly overlap with the DNS results.The simulation accuracy declines in the center region,which is similar to incompressible ODT results.The Reynolds stress,turbulent spectrum,and TKE budget terms are extracted to test the new method's performance in turbulent statistics.Based on the detailed turbulent statistics results,the physical cause of temperature fluctuations'amplification in the near-wall region for higher Mach number cases is discovered.Two typical schemes of LES subgrid closure based on one-dimensional turbulence modeling(LES-ODT)are introduced,which serves as the theoretical fundament for compressible LES-ODT development.Based on the newly developed conservative compressible ODT and canonical compressible large eddy simulation methods,a modeling methodology for compressible LES-ODT is put forward.